Writing in The Sun today, Mr Cameron said: "The cap has caused a lot fo debate so far. Bishops in the House of Lords voted to dilute it. Labour tried to obstruct it. Others have critcised it.

"I respect their concerns, but this is a plane I'm prepared to battle all he way - for three reasons. First it would restore fairness in our country.

"I've lost count of the number of people who've said: "I go to work early in the morning and on the way I pass neighbours with their curtains closed, liying in because they've chosen to live on benefits." This enfuriates people - and with good reason.

"Second the cap is going to help us crack welfare dependency. The last Government poured eye-watering amounts into welfare benefits. The result? Millions of people stuck out of work for years on end.

"Third, this is right because it ensures proper protection for the poorest. So I passionately believe this is right."

In an attempt to appease Liberal Democrats who have joined Labour ­critics of the Bill, Mr Duncan Smith is likely to offer “transitional arrangements” to help families who will be hit by the cap.

These are expected to include a new fund to help pay the moving costs of any family that cannot afford to remain living in a large home once the £26,000-a-year limit is introduced.

The minister will also offer a “grace period”, meaning that benefit claimants who have lost their jobs after years of contributing National Insurance payments through work will not immediately fall under the cap. They will be allowed to claim unlimited benefits for a period of time.

Lib Dems claim that they have been instrumental in securing the additional measures. However, Labour will oppose the Government’s amendments and table its own rival proposals — for the cap to be set at a local level, reflecting the cost of housing in different parts of the country.

The vote in the Commons comes after the Government was defeated a seventh time on the Bill in the House of Lords last night. The Lords backed an amendment put forward by Baroness Meacher, a independent peer, to limit cuts to top-up payments made to the parents of disabled children. The Government wants to introduce a slight increase to the weekly rate for the most disabled children, taking it to £77, while halving the lower rate to £27.

Lady Meacher said the Government’s plans would mean that families with a child on the lower rate would lose £1,400 a year, and warned that up to 100,000 children would be condemned to live in poverty as a result.

Lord Freud, the welfare reform minister, denied that the plan was aimed at cutting the deficit. “Every single penny of the monies is being recycled to increase support for both severely disabled children and severely disabled adults,” he said.

Government sources said ministers were determined to ensure that the reforms became law. If the Commons overturns the votes in the Lords, the Bill will return for fresh consideration in the Upper House.